- Ch 1. Basic Information about India
- Ch 2. First in India and the World
- Ch 3. Countries, Capitals & Currencies
- Ch 4. UNESCO World Heritage Sites in India
- Ch 5. International Organisations & HQ
- Ch 6. Sobriquets of India and the World
- Ch 7. National Parks & Sanctuaries
- Ch 8. Inventions and Discoveries
- Ch 9. Superlatives — India and World
- Ch 10. Sports Module
- Ch 11. Books and Authors
- Ch 12. Indian Awards and Recognition
- Ch 13. Global Awards and Recognition
- Ch 14. Indian Art and Culture
- Ch 15. Facts about Indian Polity
- Ch 16. Science and Technology
- Ch 17. Facts about Indian Geography
- Ch 18. Facts about Indian History
- Ch 1. Vedic Maths
- Ch 2. Number System
- Ch 3. Average
- Ch 4. Algebra
- Ch 5. Percentage
- Ch 6. Profit & Loss
- Ch 7. Simple & Compound Interest
- Ch 8. Chain Rule, Time & Work
- Ch 9. Ratio & Problems on Ages
- Ch 10. Time, Speed & Distance
- Ch 11. Alligation & Mixture
- Ch 12. Mensuration 2D & 3D
- Ch 13. Geometry
- Ch 14. Clock & Calendars
- Ch 15. Sets & Venn Diagram
- Ch 16. Permutation & Combination
- Ch 17. Probability
- Ch 18. Statistics
💡 Exam Tip: CUET is a multiple-choice exam. Focus on accuracy + speed. Each section is time-bound. Prioritise topics with highest frequency of appearance!
🔥 Frequently Asked | Pages 13–15
| Topic | Detail |
|---|---|
| Official Name | Republic of India / Bharat |
| Capital | New Delhi |
| Largest State (Area) | Rajasthan |
| Smallest State (Area) | Goa |
| Largest State (Population) | Uttar Pradesh |
| Smallest UT | Lakshadweep |
| Number of States | 28 States + 8 UTs |
| Longest Coastline (State) | Gujarat |
| Southernmost Point | Indira Point, Andaman & Nicobar |
| Northernmost Point | Siachen Glacier |
| National Language (Official) | Hindi (22 scheduled languages) |
| Currency | Indian Rupee (₹) |
| Parliament | Lok Sabha + Rajya Sabha + President |
| National Emblem | Lion Capital of Ashoka (Sarnath) |
| National Animal | Bengal Tiger |
| National Bird | Indian Peacock |
| National Flower | Lotus |
| National Fruit | Mango |
| National Tree | Banyan Tree |
| National River | Ganga |
| National Song | Vande Mataram |
| National Anthem | Jana Gana Mana |
- 🎯 Which is the smallest/largest state of India by area/population?
- 🎯 What is the national emblem of India?
- 🎯 Which river is declared as the National River?
🔥 HIGH Frequency Chapter | Pages 16–21
| First | Person/Place |
|---|---|
| First Prime Minister | Jawaharlal Nehru |
| First President | Dr. Rajendra Prasad |
| First Female PM | Indira Gandhi |
| First Female President | Pratibha Patil |
| First IAS Officer | Satyendranath Tagore |
| First Nobel Prize (India) | Rabindranath Tagore (Literature, 1913) |
| First to climb Everest (India) | Tenzing Norgay (1953) |
| First Indian in Space | Rakesh Sharma (1984) |
| First Female IPS Officer | Kiran Bedi |
| First Indian Woman in Space | Kalpana Chawla |
| First Five-Year Plan | 1951–56 |
| First Newspaper in India | Bengal Gazette (1780) |
| First | Detail |
|---|---|
| First Country to use Paper Currency | China |
| First Country with Postal Service | Britain |
| First Man on Moon | Neil Armstrong (1969) |
| First Woman in Space | Valentina Tereshkova (1963) |
| First Country to give women voting rights | New Zealand (1893) |
| First Computer (ENIAC) | 1945, USA |
- 🎯 Who was the first woman to become PM of India?
- 🎯 Who was the first Indian to go to space?
- 🎯 Who won India's first Nobel Prize?
📌 Moderate Frequency | Pages 22–28
| Country | Capital | Currency |
|---|---|---|
| USA | Washington D.C. | Dollar |
| UK | London | Pound Sterling |
| France | Paris | Euro |
| Germany | Berlin | Euro |
| Japan | Tokyo | Yen |
| China | Beijing | Yuan (Renminbi) |
| Russia | Moscow | Ruble |
| Australia | Canberra | Australian Dollar |
| Brazil | Brasília | Real |
| Canada | Ottawa | Canadian Dollar |
| Pakistan | Islamabad | Pakistani Rupee |
| Bangladesh | Dhaka | Taka |
| Nepal | Kathmandu | Nepalese Rupee |
| Sri Lanka | Colombo | Sri Lankan Rupee |
| Myanmar | Naypyidaw | Kyat |
| UAE | Abu Dhabi | Dirham |
| Saudi Arabia | Riyadh | Saudi Riyal |
| South Africa | Pretoria | Rand |
| Egypt | Cairo | Egyptian Pound |
| Israel | Jerusalem | Shekel |
💡 Trick: Countries using Euro — France, Germany, Italy, Spain, Netherlands, Portugal, Greece, Ireland, Belgium, Austria, Finland
- 🎯 Capital of Australia?
- 🎯 Currency of Japan?
- 🎯 Which country uses the Taka?
🔥 Frequently Asked | Pages 29–31
| Site | State | Year |
|---|---|---|
| Taj Mahal | Uttar Pradesh | 1983 |
| Agra Fort | Uttar Pradesh | 1983 |
| Fatehpur Sikri | Uttar Pradesh | 1986 |
| Red Fort Complex | Delhi | 2007 |
| Qutub Minar | Delhi | 1993 |
| Humayun's Tomb | Delhi | 1993 |
| Ajanta Caves | Maharashtra | 1983 |
| Ellora Caves | Maharashtra | 1983 |
| Elephanta Caves | Maharashtra | 1987 |
| Chola Temples | Tamil Nadu | 1987 |
| Mahabalipuram | Tamil Nadu | 1984 |
| Hampi | Karnataka | 1986 |
| Pattadakal | Karnataka | 1987 |
| Konark Sun Temple | Odisha | 1984 |
| Khajuraho Temples | Madhya Pradesh | 1986 |
| Sanchi | Madhya Pradesh | 1989 |
| Champaner-Pavagadh | Gujarat | 2004 |
| Rani-ki-Vav | Gujarat | 2014 |
| Mahabodhi Temple | Bihar | 2002 |
| Nalanda Mahavihara | Bihar | 2016 |
| Site | State |
|---|---|
| Kaziranga National Park | Assam |
| Manas Wildlife Sanctuary | Assam |
| Keoladeo Ghana NP | Rajasthan |
| Sundarbans NP | West Bengal |
| Nanda Devi & Valley of Flowers | Uttarakhand |
| Western Ghats | Multiple states |
| Great Himalayan NP | Himachal Pradesh |
- 🎯 Which is the newest UNESCO site in India?
- 🎯 Ajanta Caves are in which state?
🔥 HIGH Frequency | Pages 32–36
| Organisation | Full Form | HQ | Head |
|---|---|---|---|
| UN | United Nations | New York, USA | Secretary-General |
| UNESCO | UN Educational, Scientific & Cultural Org | Paris, France | — |
| UNICEF | UN Children's Emergency Fund | New York, USA | — |
| WHO | World Health Organisation | Geneva, Switzerland | — |
| IMF | International Monetary Fund | Washington D.C., USA | — |
| World Bank | — | Washington D.C., USA | — |
| WTO | World Trade Organisation | Geneva, Switzerland | — |
| NATO | North Atlantic Treaty Organisation | Brussels, Belgium | — |
| INTERPOL | Int'l Criminal Police Organisation | Lyon, France | — |
| ICC | International Cricket Council | Dubai, UAE | — |
| FIFA | Fédération Internationale de Football | Zurich, Switzerland | — |
| IOC | International Olympic Committee | Lausanne, Switzerland | — |
| SAARC | South Asian Assoc. for Regional Cooperation | Kathmandu, Nepal | — |
| ASEAN | Assoc. of Southeast Asian Nations | Jakarta, Indonesia | — |
| G20 | Group of 20 | No permanent HQ | — |
| OPEC | Organisation of Petroleum Exporting Countries | Vienna, Austria | — |
| ILO | International Labour Organisation | Geneva, Switzerland | — |
| IAEA | International Atomic Energy Agency | Vienna, Austria | — |
| WEF | World Economic Forum | Davos, Switzerland | — |
| Red Cross | International Committee | Geneva, Switzerland | — |
- 🎯 HQ of UNESCO / WHO / WTO?
- 🎯 SAARC Secretariat is in which city?
- 🎯 ICC headquarters?
📌 Moderate–High Frequency | Pages 37–41
| Nickname | City |
|---|---|
| City of Joy | Kolkata |
| Silicon Valley of India | Bengaluru |
| Pink City | Jaipur |
| Blue City | Jodhpur |
| Golden City | Jaisalmer |
| White City | Udaipur |
| City of Lakes | Udaipur / Bhopal |
| City of Nawabs | Lucknow / Hyderabad |
| Manchester of India | Ahmedabad |
| Detroit of India | Pithampur (MP) |
| Boston of India | Ahmedabad |
| City of Pearls | Hyderabad |
| Gateway of India | Mumbai |
| Queen of Arabian Sea | Kochi |
| Oxford of the East | Pune |
| City of Festivals | Madurai |
| Spice Garden of India | Kerala |
| Land of Five Rivers | Punjab |
| Rice Bowl of India | Andhra Pradesh / Chhattisgarh |
| Sorrow of Bihar | Kosi River |
| Nickname | Place |
|---|---|
| Land of Rising Sun | Japan |
| Land of Midnight Sun | Norway |
| Land of Thunderbolt | Bhutan |
| Roof of the World | Tibet |
| Cockpit of Europe | Belgium |
| Playground of Europe | Switzerland |
| Gift of Nile | Egypt |
| City of Canals | Venice |
| Windy City | Chicago |
📌 Moderate Frequency | Pages 42–46
| National Park | State | Known For |
|---|---|---|
| Jim Corbett NP | Uttarakhand | Tigers (First NP in India, 1936) |
| Kaziranga NP | Assam | One-horned Rhinoceros |
| Sundarbans NP | West Bengal | Royal Bengal Tigers, Mangroves |
| Gir NP | Gujarat | Asiatic Lions |
| Ranthambore NP | Rajasthan | Tigers |
| Bandhavgarh NP | Madhya Pradesh | Tigers |
| Kanha NP | Madhya Pradesh | Barasingha (Swamp Deer) |
| Periyar NP | Kerala | Elephants |
| Manas NP | Assam | Golden Langur |
| Valley of Flowers NP | Uttarakhand | Alpine Flowers |
| Namdapha NP | Arunachal Pradesh | Snow Leopard |
| Hemis NP | Ladakh | Snow Leopard (Largest NP) |
| Rajaji NP | Uttarakhand | Elephants |
| Nanda Devi NP | Uttarakhand | Alpine Ecosystem |
💡 Key Facts:
- First National Park in India: Jim Corbett (1936)
- Largest NP by Area: Hemis (Ladakh)
- Smallest NP: South Button (Andaman)
- Project Tiger launched: 1973
📌 Moderate Frequency | Pages 47–51
| Invention | Inventor | Country | Year |
|---|---|---|---|
| Telephone | Alexander Graham Bell | USA | 1876 |
| Electricity (Bulb) | Thomas Edison | USA | 1879 |
| Radio | Guglielmo Marconi | Italy | 1895 |
| Television | John Logie Baird | UK | 1926 |
| Airplane | Wright Brothers | USA | 1903 |
| Computer | Charles Babbage (concept) | UK | — |
| Internet | Tim Berners-Lee (WWW) | UK | 1991 |
| Printing Press | Johannes Gutenberg | Germany | 1440 |
| X-Ray | Wilhelm Röntgen | Germany | 1895 |
| Penicillin | Alexander Fleming | UK | 1928 |
| Vaccination | Edward Jenner | UK | 1796 |
| Diesel Engine | Rudolf Diesel | Germany | 1897 |
| Steam Engine | James Watt | UK | 1769 |
| Dynamite | Alfred Nobel | Sweden | 1867 |
| Microscope | Antonie van Leeuwenhoek | Netherlands | 1674 |
| Telescope | Galileo Galilei | Italy | 1609 |
| DNA Double Helix | Watson & Crick | UK | 1953 |
| Calculus | Newton & Leibniz | — | 1670s |
| Discovery/Invention | Contributor |
|---|---|
| Zero (0) | Brahmagupta / Aryabhata |
| Decimal System | Indian mathematicians |
| Chess | India (Chaturanga) |
| Yoga | Ancient India |
| Fibonacci Numbers (precursor) | Pingala |
🔥 HIGH Frequency | Pages 52–56
| Superlative | Answer |
|---|---|
| Largest State (Area) | Rajasthan |
| Smallest State (Area) | Goa |
| Largest State (Population) | Uttar Pradesh |
| Highest Peak | Kangchenjunga (in India) |
| Longest River | Ganga |
| Largest River Island | Majuli (Assam) |
| Largest Desert | Thar (Rajasthan) |
| Largest Lake | Wular Lake (J&K) / Chilika (saltwater) |
| Longest Coastline State | Gujarat |
| Highest Dam | Tehri Dam (Uttarakhand) |
| Highest Waterfall | Kunchikal Falls (Karnataka) |
| Largest Mosque | Jama Masjid, Delhi |
| Largest Temple | Srirangam Temple (Tamil Nadu) |
| Busiest Airport | Indira Gandhi Int'l Airport, Delhi |
| Highest Battlefield | Siachen Glacier |
| First Metro City | Kolkata (1984) |
| Superlative | Answer |
|---|---|
| Largest Country (Area) | Russia |
| Smallest Country | Vatican City |
| Most Populous Country | India |
| Tallest Mountain | Mount Everest |
| Longest River | Nile (Africa) |
| Largest Ocean | Pacific Ocean |
| Deepest Ocean | Pacific (Mariana Trench) |
| Largest Desert | Sahara (hot) / Antarctica (cold) |
| Largest Lake | Caspian Sea |
| Longest Wall | Great Wall of China |
| Tallest Building | Burj Khalifa (Dubai) |
| Largest Continent | Asia |
| Smallest Continent | Australia |
🔥 Frequently Asked | Pages 57–61
| Sport | Governing Body | Players per team |
|---|---|---|
| Cricket | ICC | 11 |
| Football | FIFA | 11 |
| Basketball | FIBA | 5 |
| Volleyball | FIVB | 6 |
| Hockey | FIH | 11 |
| Kabaddi | World Kabaddi Federation | 7 |
| Badminton | BWF | 1/2 |
| Tennis | ITF | 1/2 |
| Sport | Tournament |
|---|---|
| Cricket | ICC World Cup, IPL, Champions Trophy |
| Football | FIFA World Cup, UEFA Champions League |
| Tennis | Wimbledon, US Open, French Open, Australian Open |
| Golf | The Masters, The Open Championship |
| Chess | FIDE World Chess Championship |
| Athletics | World Athletics Championship |
| Stadium | City | Sport |
|---|---|---|
| Eden Gardens | Kolkata | Cricket |
| Wankhede | Mumbai | Cricket |
| Narendra Modi Stadium | Ahmedabad | Cricket (Largest) |
| Jawaharlal Nehru Stadium | Delhi | Multi-purpose |
| Indira Gandhi Arena | Delhi | Indoor Sports |
💡 Largest Cricket Stadium in the World: Narendra Modi Stadium, Ahmedabad (1,32,000 capacity)
📌 Moderate Frequency | Pages 62–65
| Book | Author |
|---|---|
| Discovery of India | Jawaharlal Nehru |
| India Wins Freedom | Maulana Abul Kalam Azad |
| My Experiments with Truth | Mahatma Gandhi |
| Wings of Fire | Dr. A.P.J. Abdul Kalam |
| Ignited Minds | Dr. A.P.J. Abdul Kalam |
| Gitanjali | Rabindranath Tagore |
| Gora | Rabindranath Tagore |
| Godan | Munshi Premchand |
| Train to Pakistan | Khushwant Singh |
| Midnight's Children | Salman Rushdie |
| The God of Small Things | Arundhati Roy |
| A Suitable Boy | Vikram Seth |
| 2 States | Chetan Bhagat |
| The White Tiger | Aravind Adiga |
| Book | Author |
|---|---|
| Harry Potter | J.K. Rowling |
| The Alchemist | Paulo Coelho |
| 1984 | George Orwell |
| To Kill a Mockingbird | Harper Lee |
| The Old Man and the Sea | Ernest Hemingway |
| Anna Karenina | Leo Tolstoy |
🔥 HIGH Frequency | Pages 66–69
| Award | Given for |
|---|---|
| Bharat Ratna | Exceptional service to the nation |
| Padma Vibhushan | Distinguished service of exceptional order |
| Padma Bhushan | Distinguished service of high order |
| Padma Shri | Distinguished service |
💡 First Bharat Ratna recipients (1954): C. Rajagopalachari, S. Radhakrishnan, C.V. Raman
| Award | Level |
|---|---|
| Param Vir Chakra | Highest military honour |
| Maha Vir Chakra | 2nd highest |
| Vir Chakra | 3rd highest |
| Ashoka Chakra | Highest peacetime gallantry |
| Award | Given to |
|---|---|
| Khel Ratna (Dhyan Chand) | Best sportsperson (highest) |
| Arjuna Award | Outstanding sport performance |
| Dronacharya Award | Outstanding coaches |
| Dhyan Chand Award | Lifetime contribution to sports |
📌 Moderate Frequency | Pages 70–73
| Category | Given by |
|---|---|
| Physics, Chemistry, Medicine, Literature, Peace | Respective committees in Sweden/Norway |
| Economics | Sveriges Riksbank Prize (not original Nobel) |
| Name | Category | Year |
|---|---|---|
| Rabindranath Tagore | Literature | 1913 |
| C.V. Raman | Physics | 1930 |
| Har Gobind Khorana | Medicine | 1968 |
| Mother Teresa | Peace | 1979 |
| Amartya Sen | Economics | 1998 |
| V.S. Naipaul | Literature | 2001 |
| Venkataraman Ramakrishnan | Chemistry | 2009 |
| Kailash Satyarthi | Peace | 2014 |
| Award | Given for |
|---|---|
| Pulitzer Prize | Journalism & Arts (USA) |
| Booker Prize | Best novel (Commonwealth) |
| Grammy | Music (USA) |
| Oscar | Films (USA) |
| Palme d'Or | Best film at Cannes Festival |
| Man Booker International | Translated literature |
| Ramon Magsaysay | Asian version of Nobel |
📌 Moderate Frequency | Pages 74–77
| Dance Form | State |
|---|---|
| Bharatnatyam | Tamil Nadu |
| Kathak | Uttar Pradesh / Rajasthan |
| Odissi | Odisha |
| Kuchipudi | Andhra Pradesh |
| Manipuri | Manipur |
| Mohiniyattam | Kerala |
| Kathakali | Kerala |
| Sattriya | Assam |
| Dance | State |
|---|---|
| Bihu | Assam |
| Garba | Gujarat |
| Dandiya | Gujarat |
| Ghoomar | Rajasthan |
| Bhangra | Punjab |
| Lavani | Maharashtra |
| Chhau | West Bengal / Jharkhand / Odisha |
- Hindustani Music — North India (Ragas: Bhairav, Yaman, etc.)
- Carnatic Music — South India
| Festival | Associated Region/Religion |
|---|---|
| Diwali | Pan-India (Hindu) |
| Holi | North India |
| Eid ul-Fitr | Muslim |
| Christmas | Christian |
| Baisakhi | Punjab (Sikh) |
| Pongal | Tamil Nadu |
| Onam | Kerala |
| Durga Puja | West Bengal |
| Ganesh Chaturthi | Maharashtra |
| Hemis | Ladakh (Buddhist) |
🔥 HIGH Frequency | Pages 78–82
| Fact | Detail |
|---|---|
| Adopted | 26 November 1949 |
| Enforced | 26 January 1950 |
| Father of Constitution | Dr. B.R. Ambedkar |
| Type | Written, Quasi-federal |
| Total Articles (original) | 395 |
| Total Schedules | 12 |
| Borrowed from USA | Fundamental Rights, Judicial Review |
| Borrowed from UK | Parliamentary system, Rule of Law |
| Borrowed from Ireland | Directive Principles of State Policy |
| Borrowed from Canada | Federal structure |
| Borrowed from Australia | Concurrent List |
| Article | Subject |
|---|---|
| Article 14 | Right to Equality |
| Article 19 | Freedom of Speech & Expression |
| Article 21 | Right to Life and Personal Liberty |
| Article 32 | Right to Constitutional Remedies |
| Article 44 | Uniform Civil Code (DPSP) |
| Article 51A | Fundamental Duties |
| Article 356 | President's Rule |
| Article 370 | Special status to J&K (now abrogated) |
| Position | Term | Elected by |
|---|---|---|
| President | 5 years | Electoral College |
| Vice President | 5 years | Parliament members |
| PM | No fixed term | Majority in Lok Sabha |
| Chief Justice | Till 65 years of age | — |
📌 Moderate–High Frequency | Pages 83–90
| Mission | Details |
|---|---|
| Chandrayaan-1 | 2008 — discovered water on Moon |
| Chandrayaan-2 | 2019 — Orbiter (operational), Lander (Vikram) |
| Chandrayaan-3 | 2023 — Successful Moon landing (South Pole) |
| Mangalyaan (MOM) | 2014 — First Asian Mars mission, first attempt |
| Aditya-L1 | 2023 — Solar observation satellite |
| GSLV, PSLV | Indian launch vehicles |
| Topic | Key Point |
|---|---|
| Speed of Light | 3 × 10⁸ m/s |
| Speed of Sound | 343 m/s (in air) |
| Gravity (g) | 9.8 m/s² |
| Boiling Point of Water | 100°C / 212°F |
| Freezing Point | 0°C / 32°F |
| Absolute Zero | -273.15°C |
| DNA | Deoxyribonucleic Acid |
| First Indian Satellite | Aryabhata (1975) |
- Largest Organ: Skin
- Largest Gland: Liver
- Hardest substance in body: Tooth enamel
- Smallest bone: Stapes (ear)
- Longest bone: Femur (thigh)
- Normal body temperature: 37°C / 98.6°F
🔥 Frequently Asked | Pages 91–95
| River | Origin | Empties into |
|---|---|---|
| Ganga | Gangotri Glacier | Bay of Bengal |
| Yamuna | Yamunotri Glacier | Ganga (Prayagraj) |
| Brahmaputra | Tibet (Angsi Glacier) | Bay of Bengal |
| Indus | Tibet | Arabian Sea |
| Godavari | Nashik, Maharashtra | Bay of Bengal |
| Krishna | Mahabaleshwar | Bay of Bengal |
| Cauvery | Coorg, Karnataka | Bay of Bengal |
| Narmada | Amarkantak, MP | Arabian Sea |
| Tapti | Multai, MP | Arabian Sea |
| Range | Location |
|---|---|
| Himalayas | North India |
| Karakoram | J&K / Ladakh |
| Aravalli | Rajasthan (oldest range in India) |
| Vindhya Range | Central India |
| Satpura Range | MP / Maharashtra |
| Western Ghats | West Coast |
| Eastern Ghats | East Coast |
| Pass | State | Connects |
|---|---|---|
| Nathu La | Sikkim | India–China |
| Shipki La | Himachal | India–China |
| Rohtang Pass | Himachal | Kullu–Lahaul |
| Banihal Pass | J&K | Jammu–Kashmir Valley |
| Zoji La | J&K | Srinagar–Leh |
🔥 HIGH Frequency | Pages 96–102
| Period | Details |
|---|---|
| Indus Valley Civilization | 2500–1700 BCE, Harappa & Mohenjo-daro |
| Vedic Age | 1500–600 BCE |
| Maurya Empire | 322–185 BCE (Chandragupta, Ashoka) |
| Gupta Empire | 320–550 CE (Golden Age) |
| Mughal Empire | 1526–1857 |
| Year | Event |
|---|---|
| 1857 | First War of Independence (Sepoy Mutiny) |
| 1885 | Indian National Congress founded |
| 1905 | Partition of Bengal (Lord Curzon) |
| 1906 | Muslim League founded |
| 1919 | Jallianwala Bagh massacre |
| 1920 | Non-Cooperation Movement |
| 1930 | Civil Disobedience / Dandi March |
| 1942 | Quit India Movement |
| 1947 | Independence (15 August) |
| Name | Known For |
|---|---|
| Lord Dalhousie | Doctrine of Lapse, Railways, Telegraph |
| Lord Curzon | Partition of Bengal (1905) |
| Lord Mountbatten | Last Viceroy, oversaw Partition |
| Lord Rippon | Local Self-Government, Census 1881 |
| Lord Macaulay | English Education Act 1835 |
📌 Speed Techniques | Pages 105–110
Multiplication by 11:
AB × 11 = A, (A+B), B
Example: 53 × 11 = 5, (5+3), 3 = 583
Squaring numbers ending in 5:
(X5)² = X×(X+1) | 25
Example: 75² = 7×8 | 25 = 5625
Multiplying near 100:
97 × 98 = (97-2)(98-3) | (2×3) = 95|06 = 9506
Base method multiplication: For numbers close to a base (10, 100, 1000)
98 × 97: base 100, deficits = 2 & 3;(98-3) = 95;2×3 = 06→ 9506
💡 Practice these until they're automatic — saves 30–45 seconds per calculation in the exam!
🔥 HIGH Frequency | Pages 111–125
| Type | Definition | Example |
|---|---|---|
| Natural Numbers | Counting numbers | 1, 2, 3... |
| Whole Numbers | Natural + 0 | 0, 1, 2... |
| Integers | All whole + negative | ...-2,-1,0,1,2... |
| Rational | p/q form, q≠0 | 1/2, 3/4 |
| Irrational | Cannot be expressed as p/q | √2, π |
| Prime | Divisible only by 1 and itself | 2,3,5,7,11... |
| Composite | Has factors other than 1 & itself | 4,6,8,9... |
| Divisible by | Rule |
|---|---|
| 2 | Last digit even |
| 3 | Sum of digits divisible by 3 |
| 4 | Last 2 digits divisible by 4 |
| 5 | Last digit 0 or 5 |
| 6 | Divisible by both 2 & 3 |
| 8 | Last 3 digits divisible by 8 |
| 9 | Sum of digits divisible by 9 |
| 11 | (Sum of odd-place digits) − (Sum of even-place digits) = 0 or 11 |
- HCF (GCD): Highest Common Factor — use prime factorisation or Euclid's algorithm
- LCM: Lowest Common Multiple
- Key relationship:
HCF × LCM = Product of two numbers
- 🎯 Find HCF/LCM of given numbers
- 🎯 Which of these is prime?
- 🎯 Find the remainder when X is divided by Y
🔥 Frequently Asked | Pages 126–130
Average = Sum of all values / Number of values
If a new member joins a group:
New Sum = Old Average × Old Count + New Value New Average = New Sum / New Count
Weighted Average:
Weighted Avg = (n₁×A₁ + n₂×A₂) / (n₁ + n₂)
- Average of first N natural numbers = (N+1)/2
- Average of first N even numbers = N+1
- Average of first N odd numbers = N
- Average of N consecutive numbers = (First + Last)/2
- 🎯 Average age of a group — one member leaves/joins
- 🎯 Average marks of students
- 🎯 Average speed of a journey (use harmonic mean if equal distances)
📌 Moderate–High Frequency | Pages 131–139
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b)(a - b) = a² - b²
(a + b)³ = a³ + 3a²b + 3ab² + b³
(a - b)³ = a³ - 3a²b + 3ab² - b³
a³ + b³ = (a+b)(a²-ab+b²)
a³ - b³ = (a-b)(a²+ab+b²)
- One variable:
ax + b = 0→x = -b/a - Two variables: Solve by substitution or elimination
ax² + bx + c = 0
x = [-b ± √(b²-4ac)] / 2a
- Discriminant (D) = b²-4ac:
- D > 0 → Two real distinct roots
- D = 0 → Two equal real roots
- D < 0 → No real roots
- 🎯 Find value of expression using identities
- 🎯 Solve simultaneous equations
- 🎯 Nature of roots of quadratic equation
🔥 HIGH Frequency | Pages 140–144
Percentage = (Value / Total) × 100
% Change = [(New - Old) / Old] × 100
| Fraction | Percentage |
|---|---|
| 1/2 | 50% |
| 1/3 | 33.33% |
| 1/4 | 25% |
| 1/5 | 20% |
| 1/6 | 16.67% |
| 1/8 | 12.5% |
| 1/10 | 10% |
| 3/4 | 75% |
| 2/3 | 66.67% |
- If A is x% more than B → B is
[x/(100+x)] × 100% less than A - If price increases by x% → to restore original: decrease by
[x/(100+x)] × 100% - Successive % change: If +a% then +b% → Net change =
a + b + ab/100%
- 🎯 A's salary is 20% more than B's. By what % is B's salary less than A's?
- 🎯 Price increased by 20%, by what % should consumption decrease to maintain expenditure?
- 🎯 If 40% of X = 60% of Y, find X:Y
🔥 HIGH Frequency | Pages 145–150
Profit = SP - CP
Loss = CP - SP
Profit% = (Profit / CP) × 100
Loss% = (Loss / CP) × 100
SP = CP × (100 + Profit%) / 100
CP = SP × 100 / (100 + Profit%)
Discount = MP - SP
Discount% = (Discount / MP) × 100
SP = MP × (100 - Discount%) / 100
- Two items at same SP, one at x% profit, other at x% loss:
Overall Loss% =
(x/10)²%
- 🎯 Article sold at 20% profit. Find CP if SP = ₹240
- 🎯 Marked price, successive discounts
- 🎯 Dishonest trader uses false weights — calculate actual profit%
🔥 Frequently Asked | Pages 151–155
Simple Interest (SI):
SI = (P × R × T) / 100
Amount = P + SI
Compound Interest (CI):
A = P × (1 + R/100)ⁿ
CI = A - P
When compounded half-yearly:
A = P × (1 + R/200)^(2n)
| SI | CI | |
|---|---|---|
| Interest on | Principal only | Principal + Interest |
| Growth | Linear | Exponential |
| Formula | PTR/100 | P(1+r/100)ⁿ - P |
- CI - SI for 2 years =
P × (R/100)² - CI - SI for 3 years =
P × (R/100)² × (R/100 + 3)
- 🎯 Find CI on ₹5000 at 10% for 2 years compounded annually
- 🎯 In how many years will ₹1000 double at 10% SI?
- 🎯 Difference between CI and SI for 2 years
🔥 HIGH Frequency | Pages 156–164
Work done = Rate × Time
If A can do a job in n days → A's 1 day work = 1/n
A and B together:
Combined rate = 1/A + 1/B
Time together = AB / (A+B)
Efficiency Method:
- Assume total work = LCM of given days
- Find daily work rate of each person
- Solve accordingly
- Direct proportion: More men → More work (or less time)
- Inverse proportion: More men → Less time
Formula: M₁ × D₁ × H₁ / W₁ = M₂ × D₂ × H₂ / W₂
(M=Men, D=Days, H=Hours, W=Work)
- Inlet pipe fills → positive work
- Outlet pipe drains → negative work
- Same formulas as Time & Work apply
- 🎯 A does work in 12 days, B in 15 days. Together?
- 🎯 Pipe A fills in 6 hrs, B empties in 8 hrs. Both open — time to fill?
- 🎯 15 men do work in 20 days. How many men for 10 days?
🔥 Frequently Asked | Pages 165–173
a : b = a/b
If a:b = m:n and b:c = p:q
Then a:b:c = mp : np : nq
Proportions:
- Direct: a/b = c/d → ad = bc
- Inverse: ab = cd
Key approach: Let present age = x, set up equation from conditions
Common patterns:
- "A is twice as old as B" → A = 2B
- "10 years later, A will be..." → Use (A + 10)
- "10 years ago, ratio was..." → Use (A - 10) : (B - 10)
💡 Trick: Always define variable as present age and translate each condition into an equation
- 🎯 Father's age is 3 times son's. After 12 years, twice. Find present ages.
- 🎯 Ratio of ages of A:B = 3:5. After 4 years = 2:3. Find present ages.
🔥 HIGH Frequency | Pages 174–183
Speed = Distance / Time
Distance = Speed × Time
Time = Distance / Speed
Unit Conversion:
km/h → m/s: multiply by 5/18
m/s → km/h: multiply by 18/5
- Same distance at speeds S₁ & S₂:
Average Speed = 2S₁S₂ / (S₁ + S₂) [Harmonic Mean]
- Train crossing a pole/person:
Time = Train Length / Speed - Train crossing a platform:
Time = (Train + Platform Length) / Speed - Two trains (opposite directions):
Relative Speed = S₁ + S₂ - Two trains (same direction):
Relative Speed = S₁ - S₂
Downstream speed = Boat speed + Stream speed
Upstream speed = Boat speed - Stream speed
Boat speed = (Downstream + Upstream) / 2
Stream speed = (Downstream - Upstream) / 2
- 🎯 A train 200m long passes a bridge 300m long in 25 sec. Speed?
- 🎯 Two trains approach each other at 60 & 80 km/h — time to meet?
- 🎯 Boat upstream vs downstream time problems
📌 Moderate Frequency | Pages 184–190
To mix two ingredients at prices C₁ and C₂ to get mean price Cm:
Ratio = (C₂ - Cm) : (Cm - C₁)
Diagram:
C₁ C₂
\ /
\ /
Cm
/ \
(C₂-Cm) (Cm-C₁)
If container has x litres of liquid A, and y litres is removed & replaced with liquid B repeatedly n times:
Remaining A = x × [(x-y)/x]ⁿ
- 🎯 Mix milk worth ₹25/L and ₹35/L to get ₹30/L — ratio?
- 🎯 40L mixture (milk:water = 3:1). How much water to add for 1:1?
🔥 HIGH Frequency | Pages 191–198
| Shape | Area | Perimeter |
|---|---|---|
| Square (side a) | a² | 4a |
| Rectangle (l×b) | l×b | 2(l+b) |
| Triangle (b,h) | ½×b×h | sum of sides |
| Equilateral Triangle (a) | (√3/4)a² | 3a |
| Circle (r) | πr² | 2πr |
| Semi-circle | πr²/2 | πr + 2r |
| Trapezium | ½(a+b)×h | sum of sides |
| Parallelogram | b×h | 2(a+b) |
| Rhombus | ½×d₁×d₂ | 4a |
| Shape | Volume | Surface Area |
|---|---|---|
| Cube (a) | a³ | 6a² |
| Cuboid (l,b,h) | l×b×h | 2(lb+bh+hl) |
| Cylinder (r,h) | πr²h | 2πr(r+h) |
| Cone (r,h,l) | ⅓πr²h | πr(r+l) |
| Sphere (r) | (4/3)πr³ | 4πr² |
| Hemisphere | (2/3)πr³ | 3πr² |
💡
π = 22/7 ≈ 3.14
📌 Moderate–High Frequency | Pages 199–211
Triangles:
- Sum of angles = 180°
- Pythagoras:
a² + b² = c²(right triangle) - Exterior angle = sum of opposite interior angles
- Triangle inequality: Sum of any two sides > third side
Pythagorean Triplets (memorise): (3,4,5), (5,12,13), (8,15,17), (7,24,25), (6,8,10)
Circle:
- Angle at centre = 2 × angle at circumference
- Angle in semicircle = 90°
- Equal chords are equidistant from centre
- Tangent is perpendicular to radius at point of contact
Parallel Lines:
- Corresponding angles are equal
- Alternate interior angles are equal
- Co-interior angles are supplementary (sum = 180°)
- 🎯 Find unknown angle in triangle/circle
- 🎯 Apply Pythagoras theorem
- 🎯 Chord/tangent properties
📌 Moderate Frequency | Pages 212–216
Angle between hands:
Angle = |30H - 5.5M| (where H = hours, M = minutes)
Hands coincide: Every 65 5/11 minutes Hands at 90°: 22 times in 12 hours Hands opposite (180°): 11 times in 12 hours
Clock gains/loses:
- Correct time vs clock time problems — use ratio approach
Odd days concept:
- Ordinary year (365 days) = 1 odd day
- Leap year (366 days) = 2 odd days
- 100 years = 5 odd days
- 200 years = 3 odd days
- 400 years = 0 odd days
Day codes: Sun=0, Mon=1, Tue=2, Wed=3, Thu=4, Fri=5, Sat=6
Leap Year Rule:
- Divisible by 4 → Leap year (exception: century years)
- Century year → must be divisible by 400
- 🎯 What angle between clock hands at 3:20?
- 🎯 January 1, 2020 is Wednesday. What day is January 1, 2021?
- 🎯 If today is Friday, what day will it be after 50 days?
📌 Moderate Frequency | Pages 217–221
Union of two sets:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
Union of three sets:
n(A ∪ B ∪ C) = n(A) + n(B) + n(C)
- n(A∩B) - n(B∩C) - n(A∩C)
+ n(A∩B∩C)
Only A = n(A) - n(A∩B) - n(A∩C) + n(A∩B∩C)
- Draw and fill from innermost region outward
- "Only A" = A minus overlaps
- "Exactly 2" = sum of pairs minus 3×triple overlap
- 🎯 In a class, 40 like cricket, 30 like football, 10 like both. How many like at least one?
- 🎯 Three-set Venn diagram questions with given data
🔥 HIGH Frequency | Pages 222–226
n! = n × (n-1) × ... × 2 × 1
P(n,r) = nPr = n! / (n-r)! [Arrangement/Permutation]
C(n,r) = nCr = n! / [r!(n-r)!] [Selection/Combination]
Key properties:
nCr = nC(n-r)nC0 = nCn = 1nC1 = nnPr = nCr × r!
- Permutation (P): Order MATTERS (arrange, seat, form words, fill posts)
- Combination (C): Order does NOT matter (select, choose, form committees)
| Problem | Formula |
|---|---|
| Arrange n distinct items | n! |
| Select r from n | nCr |
| Arrange n with r identical | n!/r! |
| Circular arrangement of n | (n-1)! |
| Words from letters of a word | Apply P with repetitions |
- 🎯 How many 4-letter words from CUET (no repetition)?
- 🎯 Committee of 3 men, 2 women from 6 men & 5 women?
- 🎯 In how many ways can 5 people sit in a circle?
🔥 HIGH Frequency | Pages 227–230
P(Event) = Favourable outcomes / Total outcomes
0 ≤ P(E) ≤ 1
P(E) + P(E') = 1 [Complement rule]
For mutually exclusive events:
P(A or B) = P(A) + P(B)
For independent events:
P(A and B) = P(A) × P(B)
General Addition Rule:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
| Experiment | Total outcomes |
|---|---|
| Toss 1 coin | 2 |
| Toss 2 coins | 4 |
| Toss 3 coins | 8 |
| Roll 1 die | 6 |
| Roll 2 dice | 36 |
| Draw card from deck | 52 |
- Total cards: 52
- Suits: 4 (Hearts ♥, Diamonds ♦, Clubs ♣, Spades ♠)
- Each suit: 13 cards (A, 2-10, J, Q, K)
- Red cards: 26 (Hearts + Diamonds)
- Black cards: 26 (Clubs + Spades)
- Face cards (J, Q, K): 12
- 🎯 P(drawing a king from a deck)?
- 🎯 P(sum = 7 when 2 dice rolled)?
- 🎯 P(at least one head when 3 coins tossed)?
📌 Moderate Frequency | Pages 231–237
Mean (Arithmetic Average):
Mean = Σx / n
Median: Middle value when data sorted
- Odd n: Middle term = [(n+1)/2]th term
- Even n: Average of (n/2)th and (n/2+1)th terms
Mode: Most frequently occurring value
Relationship: Mode = 3 Median - 2 Mean (empirical formula)
Range = Max - Min
Variance = Σ(x - mean)² / n
Standard Deviation (σ) = √Variance
- Class interval: Range of each group
- Class mark (midpoint): (Upper + Lower) / 2
- Cumulative frequency: Running total
- Histogram: Bar graph for continuous data (no gaps)
- Bar Chart: Discrete data (with gaps)
- Pie Chart: Parts of a whole (total = 360°)
- Ogive: Cumulative frequency curve
- 🎯 Find median of given dataset
- 🎯 Mode of a frequency distribution
- 🎯 Calculate mean from grouped data
| Section | Strategy |
|---|---|
| GK | Attempt all — pure memory, no calculation needed |
| Quant | Skip and come back — don't get stuck |
| Overall | Keep 5–10 min for review at end |
- ✅ Firsts in India & World
- ✅ International Org + HQ
- ✅ Superlatives (Largest/Smallest/Highest)
- ✅ Freedom Movement Dates
- ✅ UNESCO Heritage Sites
- ✅ Important Articles of Constitution
- ✅ Nobel Prize Winners (Indians)
- ✅ Percentage
- ✅ Profit & Loss
- ✅ Time, Speed & Distance
- ✅ Time & Work
- ✅ Simple & Compound Interest
- ✅ Permutation & Combination
- ✅ Probability
| Day | Focus |
|---|---|
| Day 1 | GK: Ch 1–6 (India basics, Firsts, Countries, UNESCO) |
| Day 2 | GK: Ch 7–13 (NP, Awards, Sports, Books, Inventions) |
| Day 3 | GK: Ch 14–18 (Art, Polity, Sci-Tech, Geography, History) |
| Day 4 | Quant: Ch 1–6 (Vedic, Numbers, Average, Algebra, %, P&L) |
| Day 5 | Quant: Ch 7–12 (Interest, Work, Ratio, Speed, Mixture, Mensuration) |
| Day 6 | Quant: Ch 13–18 (Geometry, Clocks, Sets, P&C, Probability, Stats) |
| Day 7 | Full Mock Test + Weak Areas Revision |
💖 You've got this! Consistent revision + practice = success. All the best! 🌟